Algebra Equations Quiz
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Questions and Answers

What is the solution to the equation $2(5x + 14) = 6$?

  • $-7$ (correct)
  • $-3$
  • $0$
  • $-1$

    • What is the value of $x$ in the equation $3(4 - x) = 33$?

  • $5$ (correct)
  • $3$
  • $-5$
  • $11$

    • What value of $x$ satisfies $2(3x - 4) = 4x + 17$?

  • $7$ (correct)
  • $8$
  • $-5$
  • $9$

    • In the equation $(x - 2) + 10 = 4 - 3x$, what is the value of $x$?

    <p>$5$ (B)</p> Signup and view all the answers

    If the perimeter of a rectangle is 44 meters and one dimension is 3 meters, what is the value of $x$ if the other dimension is $(1 + x)$ meters?

    <p>$14$ (A)</p> Signup and view all the answers

    What is the first step in solving the equation $3(3x + 2) = 42$?

    <p>Distribute 3 across the terms in parentheses (B)</p> Signup and view all the answers

    In the equation $2(x-5) = 2(3x-(5))$, what property allows us to eliminate the factor of 2 from both sides?

    <p>Multiplicative property of equality (D)</p> Signup and view all the answers

    What is the correct solution to the equation $-2(-6 - k) = (k + 13)$?

    <p>$k = 7$ (C)</p> Signup and view all the answers

    Which step is necessary for checking the solution of $x$ after solving an equation?

    <p>Write the original equation with the calculated value substituted in (B)</p> Signup and view all the answers

    What algebraic property is primarily used to isolate the variable in equations like $3(3x + 2) = 42$?

    <p>Inverse operations (C)</p> Signup and view all the answers

    Flashcards

    Equation

    A mathematical statement that shows two expressions are equal using the equals sign (=).

    Variable

    A symbol, usually a letter, that represents an unknown value in an equation.

    Solve for the variable

    To find the value of the unknown variable in an equation.

    Word Problem

    A problem that requires translating a real-world situation into a mathematical equation.

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    Algebraic Operations

    A method for solving equations where you perform the same operation on both sides of the equation to maintain equality.

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    What is an equation?

    A mathematical statement that includes an unknown variable (represented by a letter, like 'x' or 'k') and an equals sign. The goal is to find the value of the variable that makes the equation true.

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    What is the Distributive Property?

    It's a property used to simplify equations with parentheses. To apply the distributive property, multiply the number outside the parentheses by each term inside the parentheses.

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    How to isolate a variable in an equation?

    The goal is to get the variable (like 'x' or 'k') by itself on one side of the equation. This is done by performing opposite operations on both sides of the equation to undo any operations affecting the variable.

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    What is verification in equation solving?

    This is the final step in solving an equation. Substituting the value you found for the variable back into the original equation. Both sides of the equation should be equal if you've solved correctly.

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    What are opposite operations in equation solving?

    Opposite operations are used to isolate the variable. If the variable is being multiplied, you divide by that number on both sides. If the variable is being added to a number, you subtract that number from both sides.

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